Surely Hawaiian must come close: 5 vowels (a i u e o) and 8 consonants
(h, k, l, m, n, p, w, and glottal stop). Depending on how you write it
(long vowels doubled, or with a macron), and glottal stop omitted or
(more correctly) using U+02BB (or ASCII "'" in a pinch), you might need
more or fewer characters, but in any case, it isn't many.